Rewrite as a simplified fraction. ${0.\overline{31} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 31.3131...\\ 1x &= 0.3131...\end{align*}}$ Subtracting the two equations, we have: ${99x = 31}$ ${x = \dfrac{31}{99}} $